Find the acceleration of the ball in iˆi^ and jˆj^ form. Identify all forces on the cup and the reaction to each force. A truck collides with a car, and during the collision, the net force on each vehicle is essentially the force exerted by the other. What does the floor exert a normal force on? (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest? The mass of the drone is 1.50 kg, and its velocity is 3.00 \(\hat{i}\) m/s. What is the magnitude of the force that motorcycle exerts backward on the ground to produce its acceleration if the mass of the motorcycle with rider is 245 kg? A cleaner pushes a 4.50-kg laundry cart in such a way that the net external force on it is 60.0 N. Calculate the magnitude of his cart’s acceleration. Compare this with his weight using a ratio. If it could, calculate the magnitude of its acceleration. University Physics Volume 1 by OpenStax is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

For more information contact us at or check out our status page at (b) By exerting a force on the astronaut, the vehicle in which she orbits experiences an equal and opposite force. (a) What is the acceleration of the piano up the ramp? (b) If his mass is 90.0 kg and he accelerates at 5.00m/s2,5.00m/s2, what is the magnitude of his applied force? A particle of mass 2.0 kg is acted on by a single force \(\vec{F}_{1}\) = 18 \(\hat{i}\) N. (a) What is the particle’s acceleration? Force \(\vec{F}_{B}\) has twice the magnitude of force \(\vec{F}_{A}\). Plug in the numbers: Fpush = 383 + 180 = 563 N. You’re dragging your little brother up the 25-degree wheelchair ramp at the doctor’s office. (b) What force does the winning player exert on the ground to move forward if his mass plus equipment is 110.0 kg? Two small forces, \(\vec{F}_{1}\) = −2.40 \(\hat{i}\) − 6.10t \(\hat{j}\) N and \(\vec{F}_{2}\) = 8.50 \(\hat{i}\) − 9.70 \(\hat{j}\) N, are exerted on a rogue asteroid by a pair of space tractors. (b) What is the amount of stretch of spring A from the rest position? Draw a free-body diagram; be sure to include the friction of the road that opposes the forward motion of the car. As the truck slows down, the crate continues to move forward at constant speed. The truck bed is frictionless and the crate is not in contact with any other surface, so there are no horizontal forces. (a) Calculate the tension in a vertical strand of spider web if a spider of mass 2.00×10−5kg2.00×10−5kg hangs motionless on it. A rock is thrown straight up.

If the body accelerates to the left at 20 m/s, A force acts on a car of mass m so that the speed v of the car increases with position x as v = kx. The figure shows a box on a ramp. (c) If the object begins from rest, find its speed after 5.00 s. (d) Find the components of the velocity of the object after 5.00 s. In a particle accelerator, a proton has mass 1.67×10−27kg1.67×10−27kg and an initial speed of 2.00×105m/s.2.00×105m/s. Inertia is the tendency of an object to remain at rest or remain in motion.

Identify each force on each book with a double subscript notation (for instance, the contact force of the history book pressing against physics book can be described as \(\vec{F}_{HP}\)), and determine the value of each of these forces, explaining the process used.

That is, what do we apply? Find the third force \(\vec{F}_{3}\) that is needed to balance the first two forces. (a) Find the acceleration vector in terms of m. (b) Find the mass of the object. As shown below, two identical springs, each with the spring constant 20 N/m, support a 15.0-N weight. (b) What is the magnitude of the force exerted on the ship by the artillery shell, and why? (b) Calculate the acceleration. The sled has a horizontal component of acceleration of 5.0m/s25.0m/s2 and a downward component of 3.8m/s23.8m/s2. At the beginning of the day, the spring stretches 50 cm. a student is trying to push a fridge into a dorm room, but the fridge isn't moving. Newton's laws of motion. (a) What is the resultant (net force) of these two force vectors? Forces. The forces are coplanar (in the same plane). How much will the spring stretch if the suspended mass is 530.0 g? (See the free-body diagram.) Two equal and opposite forces do not cancel because they act on different systems. Shown below is a 30.0-kg block resting on a frictionless ramp inclined at 60°60° to the horizontal. A telephone pole has three cables pulling as shown from above, with \(\vec{F}_{1}\) = (300.0 \(\hat{i}\) + 500.0 \(\hat{j}\)), \(\vec{F}_{2}\) = −200.0 \(\hat{i}\), and \(\vec{F}_{3}\) = −800.0 \(\hat{j}\). (d) Sketch the situation, indicating the system of interest used to solve each part. (a) What is the acceleration of the crate? Two teenagers are pulling on ropes attached to a tree. Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon.

(b) If the particle starts at rest, how far does it travel in the first 5.0 s? An 80.0-kg passenger in an SUV traveling at 1.00 x 10. (e) Weight is always proportional to mass. Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of 201m/s2201m/s2. Suppose that you’re struggling to get a 20.0-kg block of ice moving up a 40.0-degree ramp. (b) Did you include all forces in the overhead view in your free-body diagram? (a) Find an equation for the tension in each section of the string in terms of the variables m, g, and θθ. Describe them. Assume that each half of the line is straight. (b) What is the velocity of the piano when it reaches the top if the ramp is 4.0 m long and the piano starts from rest? (a) What is the mass of the infant and basket if a scale reading of 55 N is observed? What is the magnitude of the acceleration of the car? A body of mass m moves in a horizontal direction such that at time t its position is given by x(t) = at. According to Newton’s first law, there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. (Hint:Place all forces at the center of his body, and include his weight.) What properties do forces have that allow us to classify them as vectors?

(b) Give a revised diagram showing the xy-component form. Assume no friction or drag forces affect the vessel. Assume no friction or drag forces affect the vessel. A bullet shot from a rifle has mass of 10.0 g and travels to the right at 350 m/s. (a) Show that the tension in the line can be calculated using the equation \(T = \frac{mg}{2 \sin \theta}\). A table is placed on a rug. A force of 1600 N acts parallel to a ramp to push a 300-kg piano into a moving van. A body with a mass of 10.0 kg is assumed to be in Earth’s gravitational field with g = 9.80 m/s, A fireman has mass m; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (b) What is the time-dependent force acting on the body? The driver attempts to get the car out of the mud by exerting a perpendicular force of 610.0 N, and the distance she pushes in the middle of the rope is 1.00 m while she stands 6.00 m away from the car on the left and 6.00 m away from the tree on the right. Two ropes are attached to a tree, and forces of F⃗ 1=2.0iˆ+4.0jˆNF→1=2.0i^+4.0j^N and F⃗ 2=3.0iˆ+6.0jˆNF→2=3.0i^+6.0j^N are applied. (b) What are the magnitude and direction of the net force? A body of mass m moves in a horizontal direction such that at time t its position is given by x(t)=at4+bt3+ct,x(t)=at4+bt3+ct, wherea, b, and c are constants. It strikes a target, a large bag of sand, penetrating it a distance of 34.0 cm. Find the position of the end of the spring away from its rest position. After 10.0 s, the velocity is 9.00 \(\hat{i}\) + 4.00 \(\hat{j}\) m/s.

At the top of the trajectory, the velocity is momentarily zero. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. The center length of sting is horizontal. (b) What is the mass on the Moon? Shown below is a body of mass 1.0 kg under the influence of the forces \(\vec{F}_{A}\), \(\vec{F}_{B}\), and m\(\vec{g}\).

The driver in the previous problem applies the brakes when the car is moving at 90.0 km/h, and the car comes to rest after traveling 40.0 m. What is the net force on the car during its deceleration? Donate Login Sign up. Taking a frame attached to Earth as inertial, which of the following objects cannot have inertial frames attached to them, and which are inertial reference frames?

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